Bottom Line:
In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated.The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa.We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the 'morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.

RSTB20150129F4: Marginal posterior density plots for the phylogenetic estimate of fossil age of each of the 18 penguin fossils older than 30 Myr using Mk-8. Boxes are the superimposed age ranges derived from geological data. (Online version in colour.)

Mentions:
Mk-8 was the best-fitting model for the penguin dataset according to the analysis of Gavryushkina et al. [23]. As with Mk-1, this model produced phylogenetic estimates of fossil age that were very concordant with the geological age ranges of the fossils (figure 2b), with an overall R2 = 0.924. The median error was 2.05 Myr across all 36 fossils. In this analysis, none of the fossils exhibited any evidence (i.e. log BF < 0.0) that the phylogenetic estimate of fossil age was inconsistent with the geological age range. However, if we consider the posterior probability that the fossil is in the geological age range, then five of the 36 fossils had a posterior probability less than 0.05 for Mk-8, suggesting low posterior support for the phylogenetic estimate of fossil age being within the palaeontological age range. These five fossils were Madrynornis mirandus, Paraptenodytes antarcticus, Perudyptes devriesi, Sphenicus muizoni and Waimanu manneringi, with posterior probabilities that the phylogenetic estimate of fossil age is in the palaeontological range of 0.035, 0.018, 0.046, 0.004 and 0.037, respectively. All other fossils have posterior probabilities of more than 0.05 of their age being in the palaeontological range. Again the absolute discrepancy in the ages are quite moderate for the five fossils with low posterior probabilities, with M. mirandus: 6.7 versus 10 Myr (phylogenetic estimate of fossil age versus palaeontological age), P. antarcticus: 28.0 versus 22, P. devriesi: 49.0 versus 40, S. muizoni: 5.1 versus 9.1 and W. manneringi: 56.7 versus 61.05. A summary of all the individual estimates are tabulated in table 2. The individual marginal posterior distributions of phylogenetic estimates of fossil age under Mk-8 and the corresponding geological range are shown in figures 3 and 4.Figure 3.

RSTB20150129F4: Marginal posterior density plots for the phylogenetic estimate of fossil age of each of the 18 penguin fossils older than 30 Myr using Mk-8. Boxes are the superimposed age ranges derived from geological data. (Online version in colour.)

Mentions:
Mk-8 was the best-fitting model for the penguin dataset according to the analysis of Gavryushkina et al. [23]. As with Mk-1, this model produced phylogenetic estimates of fossil age that were very concordant with the geological age ranges of the fossils (figure 2b), with an overall R2 = 0.924. The median error was 2.05 Myr across all 36 fossils. In this analysis, none of the fossils exhibited any evidence (i.e. log BF < 0.0) that the phylogenetic estimate of fossil age was inconsistent with the geological age range. However, if we consider the posterior probability that the fossil is in the geological age range, then five of the 36 fossils had a posterior probability less than 0.05 for Mk-8, suggesting low posterior support for the phylogenetic estimate of fossil age being within the palaeontological age range. These five fossils were Madrynornis mirandus, Paraptenodytes antarcticus, Perudyptes devriesi, Sphenicus muizoni and Waimanu manneringi, with posterior probabilities that the phylogenetic estimate of fossil age is in the palaeontological range of 0.035, 0.018, 0.046, 0.004 and 0.037, respectively. All other fossils have posterior probabilities of more than 0.05 of their age being in the palaeontological range. Again the absolute discrepancy in the ages are quite moderate for the five fossils with low posterior probabilities, with M. mirandus: 6.7 versus 10 Myr (phylogenetic estimate of fossil age versus palaeontological age), P. antarcticus: 28.0 versus 22, P. devriesi: 49.0 versus 40, S. muizoni: 5.1 versus 9.1 and W. manneringi: 56.7 versus 61.05. A summary of all the individual estimates are tabulated in table 2. The individual marginal posterior distributions of phylogenetic estimates of fossil age under Mk-8 and the corresponding geological range are shown in figures 3 and 4.Figure 3.

Bottom Line:
In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated.The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa.We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the 'morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.